A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

A minimal model of quantized conductance in interacting ballistic quantum wires

We review what we consider to be the minimal model of quantized conductance in a finite interacting quantum wire. Our approach utilizes the simplicity of the equation of motion description to both deal with general spatially dependent interactions and finite wire geometry. We emphasize the role of two different kinds of boundary conditions, one associated with local "chemical" equilibrium in the sense of Landauer, the other associated with screening in the proximity of the Fermi liquid metallic leads. The relation of our analysis to other approaches to this problem is clarified. We then use our formalism to derive a Drude type expression for the low frequency AC-conductance of the finite wire with general interaction profile.Comment: 6 pages, 2 figures; extended discussion, references adde

Robust Structured Low-Rank Approximation on the Grassmannian

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identification and data series analysis. At the same time it has been shown how to control the rank of a structured approximation via matrix factorization approaches. The drawbacks of these methods either lie in the lack of robustness against outliers or in their static nature of repeated batch-processing. We present a Robust Structured Low-Rank Approximation method on the Grassmannian that on the one hand allows for fast re-initialization in an online setting due to subspace identification with manifolds, and that is robust against outliers due to a smooth approximation of the $\ell_p$-norm cost function on the other hand. The method is evaluated in online time series forecasting tasks on simulated and real-world data

Efficient radiative transfer calculation and sensor performance requirements for the aerosol retrieval by airborne imaging spectroscopy

Detailed aerosol measurements in time and space are crucial to address open questions in climate research. Earth observation is a key instrument for that matter but it is biased by large uncertainties. Using airborne imaging spectroscopy, such as ESA's upcoming airborne Earth observing instrument APEX, allows determining the widely used aerosol optical depth (AOD) with unprecedented accuracy thanks to its high spatial and spectral resolution, optimal calibration and high signal-to-noise ratios (SNR). This study was carried out within the overall aim of developing such a tropospheric aerosol retrieval algorithm. Basic and efficient radiative transfer equations were applied to determine the sensor performance requirement and a sensitivity analysis in context of the aerosol retrieval. The AOD retrieval sensitivity requirement was chosen according to the demands of atmospheric correction processes. Therefore, a novel parameterization of the diffuse path-radiance was developed to simulate the atmospheric and surface effects on the signal at the sensor level. It was found for typical remote sensing conditions and a surface albedo of less than 30% that a SNR of circa 300 is sufficient to meet the AOD retrieval sensitivity requirement at 550nm. A surface albedo around 50% requires much more SNR, which makes the AOD retrieval very difficult. The retrieval performance is further analyzed throughout the visual spectral range for a changing solar geometry and different aerosol characteristics. As expected, the blue spectral region above dark surfaces and high aerosol loadings will provide the most accurate retrieval results. In general, the AOD retrieval feasibility could be proven for the analyzed cases for APEX under realistic simulated conditions

A Consistent Dark Matter Interpretation For CoGeNT and DAMA/LIBRA

In this paper, we study the recent excess of low energy events observed by the CoGeNT collaboration and the annual modulation reported by the DAMA/LIBRA collaboration, and discuss whether these signals could both be the result of the same elastically scattering dark matter particle. We find that, without channeling but when taking into account uncertainties in the relevant quenching factors, a dark matter candidate with a mass of approximately ~7.0 GeV and a cross section with nucleons of sigma_{DM-N} ~2x10^-4 pb (2x10^-40 cm^2) could account for both of these observations. We also comment on the events recently observed in the oxygen band of the CRESST experiment and point out that these could potentially be explained by such a particle. Lastly, we compare the region of parameter space favored by DAMA/LIBRA and CoGeNT to the constraints from XENON 10, XENON 100, and CDMS (Si) and find that these experiments cannot at this time rule out a dark matter interpretation of these signals.Comment: 8 pages, 6 figure

Violent Behavior During Psychiatric Inpatient Treatment in a German Prison Hospital

Violent behavior in correctional facilities is common and differs substantially in type, target, implication, and trigger. Research on frequency and characteristics of violent behavior in correctional facilities and psychiatric hospitals is limited. Results from recent research suggest that comorbidity of severe mental disorder, personality disorder, and diagnosis of substance abuse is related to a higher risk of violent behavior. In the Berlin prison hospital, a database was created to collect data from all violent incidences (n=210) between 1997 and 2006 and between 2010 and 2016. In a retrospective, case-control study, we analyzed specific socioeconomic data and psychiatric diagnosis and compared the group of prisoners with violent behavior with randomly selected prisoners of the same department without violent behavior (n = 210). Diagnosis of schizophrenia, non-German nationality, no use of an interpreter, no children, and no previous sentence remained significantly associated with the dependent variable violent behavior. There were no significant differences regarding age and legal statuses. Practical implications for clinical work are discussed

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated